Is it possible to invert the SSS shader effect?
Following on from what Yvain commented: "negative SSS" is basically an opaque material. If the surface is opaque, you can't see through any face to see if the volume gets lighter. If what you're after isn't a surface texture, it's probably a volume texture. And if you want something lighter in the middle of a volume than the volume's outer walls, you either need an Emission or Volume Scatter node in the Volume of your material Output, or a rough Glass surface shader with a light in the volume.